On bounded symmetric domain Ω of C^n, we investigate the properties of functions in weighted Bergman spaces A^P（Ω,dvs） for 0 〈 p ≤ ＋∞ and -1 〈 s 〈 4-∞. Based on the estimate of Bergman kernel, we obtain som...On bounded symmetric domain Ω of C^n, we investigate the properties of functions in weighted Bergman spaces A^P（Ω,dvs） for 0 〈 p ≤ ＋∞ and -1 〈 s 〈 4-∞. Based on the estimate of Bergman kernel, we obtain some characterizations of functions in A^P（Ω, dvs） in terms of a class of linear operators D^αB. Making use of these characterizations, we extend A^P（Ω,dvs） to the weighted Bergman spaces Aα^p,B（Ω,dvs） in a very natural way for 1 〈 p 〈 4-∞ and any real number s, that is, -∞ 〈 s 〈 ＋∞. This unified treatment covers some classical Bergman spaces, Besov spaces and Bloch spaces. Meanwhile, the boundedness of Bergman projection operators on Aα^P,β（Ω, dvs） and the dual of Aα^P,B（Ω, dvs） are given.展开更多
The weighted graphs, where the edge weights are positive numbers, are considered. The authors obtain some lower bounds on the spectral radius and the Laplacian spectral radius of weighted graphs, and characterize the ...The weighted graphs, where the edge weights are positive numbers, are considered. The authors obtain some lower bounds on the spectral radius and the Laplacian spectral radius of weighted graphs, and characterize the graphs for which the bounds are attained. Moreover, some known lower bounds on the spectral radius and the Laplacian spectral radius of unweighted graphs can be deduced from the bounds.展开更多
The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu’s property A, the ideal structure of the Roe algebra of X with coeff...The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu’s property A, the ideal structure of the Roe algebra of X with coefficients in B(H) is completely characterized by the ideal families of weighted subspaces of X, where B(H) denotes the C*-algebra of bounded linear operators on a separable Hilbert space H.展开更多
This paper deals with the existence and multiplicity of nontrivial solutions to a weighted nonlinear elliptic system with nonlinear homogeneous boundary condition in a bounded domain. By using the Caffarelli-Kohn-Nire...This paper deals with the existence and multiplicity of nontrivial solutions to a weighted nonlinear elliptic system with nonlinear homogeneous boundary condition in a bounded domain. By using the Caffarelli-Kohn-Nirenberg inequality and variational method, we prove that the system has at least two nontrivial solutions when the parameter λ belongs to a certain subset of R.展开更多
基金the NNSF of China(10571164)the SRFDP of Higher Education(20050358052)
文摘On bounded symmetric domain Ω of C^n, we investigate the properties of functions in weighted Bergman spaces A^P（Ω,dvs） for 0 〈 p ≤ ＋∞ and -1 〈 s 〈 4-∞. Based on the estimate of Bergman kernel, we obtain some characterizations of functions in A^P（Ω, dvs） in terms of a class of linear operators D^αB. Making use of these characterizations, we extend A^P（Ω,dvs） to the weighted Bergman spaces Aα^p,B（Ω,dvs） in a very natural way for 1 〈 p 〈 4-∞ and any real number s, that is, -∞ 〈 s 〈 ＋∞. This unified treatment covers some classical Bergman spaces, Besov spaces and Bloch spaces. Meanwhile, the boundedness of Bergman projection operators on Aα^P,β（Ω, dvs） and the dual of Aα^P,B（Ω, dvs） are given.
基金supported by the National Natural Science Foundation of China(Nos.11101027,11071115,10971114,10990011,11171097)the Fundamental Research Funds for the Central Universities of China(No.2011JBM136)
文摘The weighted graphs, where the edge weights are positive numbers, are considered. The authors obtain some lower bounds on the spectral radius and the Laplacian spectral radius of weighted graphs, and characterize the graphs for which the bounds are attained. Moreover, some known lower bounds on the spectral radius and the Laplacian spectral radius of unweighted graphs can be deduced from the bounds.
基金Project supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 200416)the Program for New Century Excellent Talents in University of China (No. 06-0420)+2 种基金the Scientific Research Starting Foundation for the Returned Overseas Chinese Scholars (No.2008-890)the Dawn Light Project of Shanghai Municipal Education Commission (No. 07SG38)the Shanghai Pujiang Program (No. 08PJ14006).
文摘The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu’s property A, the ideal structure of the Roe algebra of X with coefficients in B(H) is completely characterized by the ideal families of weighted subspaces of X, where B(H) denotes the C*-algebra of bounded linear operators on a separable Hilbert space H.
文摘This paper deals with the existence and multiplicity of nontrivial solutions to a weighted nonlinear elliptic system with nonlinear homogeneous boundary condition in a bounded domain. By using the Caffarelli-Kohn-Nirenberg inequality and variational method, we prove that the system has at least two nontrivial solutions when the parameter λ belongs to a certain subset of R.
